The game you are describing is Backgammon.
The Backgammon board consists of 24 narrow triangles called points (or pips), arranged in four quadrants of six points each. The triangles alternate in color (traditionally light/dark or brown/cream).
Trivial Pursuit uses a circular wheel-shaped board with wedge-shaped spaces (not triangular points) and pie-piece tokens. Chinese Checkers uses a star-shaped board with holes (not triangles). Backgammon is the classic game defined by its 24 triangular points.